Pharmacy technician math practice: practice problems and exam questions

Pharmacy calculations for pharmacy technician exams such as the PTCE: percentage and ratio strength, dilutions and alligation, reconstitution, dosing and infusion rates.

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Topics in this course

  1. Pharmacy calculationspercentage strength and ratio strength · reconstitution and concentrations · alligationcalculations
  2. Dosage calculationstablets and liquids · weight-based doses · doses and concentrationscalculations
  3. IV infusion ratespump rate · drip rate · time and dose ratecalculations
  4. Pediatric & critical-care dosingpediatric weight-based doses (mg/kg/day divided) · heparin and insulin infusions (units/h, mL/h) · titrated drips (mcg/kg/min to mL/h)calculations

Exam tips for Pharmacy technician math practice

  • Percentage strength w/v means grams per 100 mL.
  • For alligation, the parts of each ingredient come from the opposite corner of the grid.
  • Double-check every conversion between mg, g, mL and L.

Worked examples

Pharmacy calculationsEasy
0123455 mL

A solution is 0.5% w/v. You need 9 mg of the drug. Draw up the volume in the syringe: what volume V is that?

0.5% w/v9 mg

Find V (mL)

Show hints
  1. x% w/v means x g in 100 mL.
  2. 0.5% w/v = 5 mg/mL.
  3. On this 5 mL syringe every small line is 0.1 mL.
Show the answer and the step-by-step solution

Strength to volume: turn the strength into mg per mL first. A w/v percentage is grams per 100 mL, so x% = 10x mg/mL. A ratio strength 1:n is 1 g in n mL. After reconstitution the concentration is the powder's dose over the final volume (diluent + powder volume). Then volume = dose/concentration.

Strength in mg/mL

0.5 g/100 mL = 5 mg/mL

Volume

V = 9/5 = 1.8 mL

Answer

V = 1.8 mL
Dosage calculationsMedium
17 kgBSA = 0.86 m²250 mg/m²D = ? mg

A patient weighing 17 kg has a body surface area of 0.86 m². The prescription is 250 mg/m². Find the dose D in mg.

17 kgBSA = 0.86 m²250 mg/m²

Find D (mg)

Show hints
  1. The order is per m² of body surface area.
  2. D = dose per m² × BSA. The weight is not needed.
  3. 250·0.86.
Show the answer and the step-by-step solution

Body-surface-area dosing: many cytotoxic and some paediatric doses are prescribed per square metre of body surface area: dose (mg) = dose per m² × BSA (m²). The Mosteller formula estimates BSA = √(height (cm) × weight (kg)/3600).

Dose

D = 250·0.86 = 215 mg

Answer

D = 215 mg

How practising works

  • “Practise this course” mixes problems from all its topics, like a real exam.
  • Every problem has new values, so you learn the method instead of an answer.
  • Stuck? Open a small hint first, and the full explanation only when you need it.
  • Mock exams are timed and have no hints, and you get your score and a full review at the end.

Calculators for this course

Dosage calculator (desired over have)IV flow rate and drip rate calculatorWeight-based dose calculator (mg/kg)Body surface area calculator (BSA)mcg/kg/min to mL/h calculator (weight-based infusion)Reconstitution calculator (powder volume and concentration)Pediatric safe dose range calculator (mg/kg/day)IV infusion time calculator (when will the infusion finish?)Alligation calculatorHeparin infusion rate calculator

Related courses

Nursing MathPediatric and Critical-Care DosingNCLEX-style dosage calculationsNCLEX-style practice questions (RN)Maternity NursingPharmacy CalculationsClinical PharmacokineticsNCLEX-PN-style practice questions (LPN/LVN)
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